What is the Meaning of Dualities in Perturbative Expansions?

In summary, duality hypotheses are a way of relating different physical theories and are not limited to perturbative expansions. They can involve non-perturbative effects and apply to various physical phenomena. It is important to look at the bigger picture of duality hypotheses to understand their concept better.
  • #1
metroplex021
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Hi folks,

I have been trying to get my head around dualities, and hit a stumbling block right away. Duality hypotheses are framed by thinking about perturbative expansions of interaction lagrangians ( at least when thinking about s-dualities). In such expansions, the first term is regarded as the 'classical' term, and what that means in the path integral approach is that the first term corresponds to the classical trajectory permitted by the interaction.

But then its clear the the perturbative expansion in mind in these discussions of duality cannot be the expansion about the interaction coupling and that Feynman diagrams illustrate, because there the first term is the interaction-free term - not the one describing the classically-permitted trajectory of the interacting system. So can someone tell me what I'm missing when people like Sen discuss dualities in terms of these expansions ( see eg here http://www.iisc.ernet.in/currsci/dec251999/articles20.htm) ?!

I appreciate this is going to be really obvious, but any help would be much appreciated!
 
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  • #2


Hi there,

I understand your confusion about duality hypotheses and their relation to perturbative expansions. The key thing to remember is that duality hypotheses are a way of relating seemingly different physical theories, and they are not limited to just perturbative expansions.

In fact, duality hypotheses often involve non-perturbative effects, which cannot be captured by simple Feynman diagrams. These non-perturbative effects can lead to the classical trajectory not being the dominant term in the expansion, as you pointed out.

Furthermore, duality hypotheses are not limited to just interactions between particles. They can also apply to other physical phenomena, such as symmetries and dual descriptions of the same system.

I suggest taking a step back and looking at the bigger picture of duality hypotheses, rather than getting caught up in the specifics of perturbative expansions. This will help you understand the concept better and see how it applies to a wide range of physical theories and phenomena.

I hope this helps clarify things for you. Best of luck in your studies!
 

What is a duality in science?

A duality in science refers to the concept that seemingly different or opposing ideas or phenomena can actually be interconnected or interchangeable. It suggests that there are hidden connections between different aspects of nature that may appear to be separate at first glance.

What are some examples of dualities in science?

Examples of dualities in science include wave-particle duality, which describes how particles can exhibit both wave-like and particle-like behavior; matter-energy duality, which states that matter and energy are interchangeable; and space-time duality, which relates the concepts of space and time as two aspects of the same fundamental structure.

How do dualities impact scientific understanding?

Dualities can provide new insights and bridge gaps in scientific understanding by revealing hidden connections between seemingly unrelated phenomena. They can also lead to the development of new theories and paradigms, and help to unify different branches of science.

What challenges do dualities present in scientific research?

Dualities can be difficult to reconcile with our current understanding of the world, and may challenge traditional ways of thinking. They can also be difficult to test and verify, as they often involve abstract concepts and may require advanced technology or experiments to observe.

How are dualities relevant to real-world applications?

Dualities have important practical applications in fields such as quantum mechanics, where they have led to the development of technologies such as quantum computing. They also have implications for understanding complex systems and phenomena, such as in biology and economics.

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